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Knot lattice homology and $q$-series invariants for plumbed knot complements (2403.14461v1)
Published 21 Mar 2024 in math.GT and math.QA
Abstract: We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsv\'ath, Stipsicz, and Szab\'o, and the BPS $q$-series of Gukov and Manolescu. This invariant is a natural extension of weighted graded roots of negative definite plumbed 3-manifolds introduced earlier by the first two authors and Krushkal. We prove a surgery formula relating our invariant with the weighted graded root of the surgered 3-manifold.